Arihant Expert Team Solutions for Exercise 1: Practice Questions

Ravina’s savings and expenditure are in the ratio of $2:3$. Her income increases by $10\%$. Her expenditure also increases by $12\%$. By how much per cent does her savings increase?

In a zoo, there are lions and parrots. If counted, there are $100$ heads and $290$ legs. How many parrots are there?

A butler stole wine from a butt of sherry which contains $15\%$ of spirit and he replaced what he had stolen by wine containing $6\%$ of spirit. The butt was then $9\%$ strong only. How much of the butt did he steal?

A container is filled with liquid, $6$ parts of which are water and $10$ parts milk. How much of the mixture must be drawn off and replaced with water, so that the mixture may be half water and half milk?

Two vessels $P$ and $Q$ contain wine and water in the ratios of $5:2$ and $8:5$, respectively. Find the ratio in which these mixtures are to be mixed to get a new mixture containing wine and water in the ratio of $9:4$.

A butler stole wine from a butt of sherry which contained $80\%$ of spirit and he replaced it by wine containing only $32\%$ spirit. Then, the butt was of $48\%$ strength only. How much of the butt did he steal?

$8 L$ are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is $16:65$. How much wine did the cask hold originally?

A vessel is filled with liquid $3$ parts of which are water and $5$ parts syrup. How much of the mixture must be drawn off and replaced with water, so that the mixture may be half water and half syrup?